Provide an appropriate response.
-$$x = 2 u ^ { 2 } , y = 6 u v$$
A) $24 \mathrm { u } ^ { 2 }$
B) $24 v ^ { 2 }$
C) $12 v ^ { 2 }$
D) $12 \mathrm { u } ^ { 2 }$

Question

Quizplus · Accepted Answer

The correct response is found by differentiating both $x$ and $y$ with respect to $u$, and then multiplying the derivatives according to the chain rule. Differentiating $x = 2u^2$ with respect to $u$ gives $dx/du = 4u$, and differentiating $y = 6uv$ with respect to $u$ gives $dy/du = 6v$. Multiplying these derivatives together gives $dx/du \cdot dy/du = 4u \cdot 6v = 24uv$. However, the options provided do not directly match this result due to a misunderstanding in the question's interpretation. The correct approach should involve finding a relationship that matches the given options, but based on the derivatives provided, none of the options directly relate to the differentiated forms of $x$ and $y$ as described. My explanation mistakenly assumed a direct multiplication of derivatives was sought, which does not align with the options given, indicating a misinterpretation of the task.

Provide an Appropriate Response x=2u2,y=6uvx = 2 u ^ { 2 } , y = 6 u vx=2u2,y=6uv

Provide an Appropriate Response $x = 2 u ^ { 2 } , y = 6 u v$